Asymptotics of violent surface motion

The very fact that the motion of a free boundary is violent can be of considerable value in analysing the mathematical models of its evolution. For example the smallness of the angle between the undisturbed free surface of a liquid and an impacting smooth solid almost allows the problem to be formul...

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Bibliographic Details
Published in:Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 1997-03, Vol.355 (1724), p.679-685
Main Authors: Chapman, S. J., Gillow, K. A., Howison, S. D., Ockendon, J. R.
Format: Article
Language:English
Subjects:
Body regions
Boundary conditions
Flow velocity
Fluids
Free boundaries
Interfacial tension
Liquids
Mathematical surfaces
Mathematics
Velocity
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Summary:The very fact that the motion of a free boundary is violent can be of considerable value in analysing the mathematical models of its evolution. For example the smallness of the angle between the undisturbed free surface of a liquid and an impacting smooth solid almost allows the problem to be formulated as a classical 'mixed boundary value' problem. This paper gives an informal review ofseveral such configurations and indicates where the violence of the motion enables asymptotic analysis to give new insight, both qualitatively and quantitatively. However, many of these situations are in practice irreversible and we will explain why this can cause severe difficulties with the mathematics.
ISSN:1364-503X
1471-2962
DOI:10.1098/rsta.1997.0033